Speaker: Marco Abbadini
Wednesday, 4 January 2023, 14:00, visio link: https://zoom.us/j/97278780690?pwd=cGU5Yi9UVTk0aXhndWtuanY4dHp0QT09
Abstract: Compact Hausdorff spaces are the topological abstraction of the unit interval [0,1] (in a sense that can be made precise). Let us now equip the unit interval with the "denominator map" den: [0,1] -> N that maps a rational number to its denominator and an irrational number to 0. We characterize the abstraction of [0,1] that takes into account both the topology and the denominator map.
(We use this result to provide a representation theorem for a class of lattice-ordered groups, generalizing a result of M.H. Stone (1941).)